Analysis and modeling of the behavior of exponentially graded cantilever beams loaded by various parabolic distribution loads

This paper investigates the plane stress problem of a cantilever beam subjected to variable loading in bending. The material properties of the beam vary continuously through thickness, according to an exponential distribution. The study proposes a high-order Airy function related to parabolic loading boundary conditions, based on compatibility equations. A mathematical formulation with parameters based on parabolic loading is developed, and a numerical application presented to evaluate the influence of different parameters on the objectives. The solution obtained satisfactory results, indicating its potential for structural calculations.